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eISSN 0454-8124
pISSN 1225-6951

### Original Article

Kyungpook Mathematical Journal 2010; 50(1): 117-122

Published online March 23, 2010

### 1-(2-) Prime Ideals in Semirings

Pandarinathan Nandakumar

Department of Mathematics, Perunthalaivar Kamarajar Institute of Engineering and Technology, (Government of Puducherry Institution), Nedungadu, Karaikal - 609 603 (U. T. of Puducherry), India

Received: March 23, 2010; Revised: March 23, 2010; Accepted: March 23, 2010

### Abstract

In this paper, we introduce the concepts of 1-prime ideals and 2-prime ideals in semirings. We have also introduced $m_{1}$-system and $m_{2}$-system in semiring. We have shown that if $Q$ is an ideal in the semiring $R$ and if $M$ is an $m_{2}$-system of $R$ such that $overline{Q} igcap M = emptyset$ then there exists as 2-prime ideal $P$ of $R$ such that $Q subseteq P$ with $Pigcap M = emptyset.$}

Keywords: Semirings, Prime ideal, Semiprime ideal